Proceedings ArticleDOI
Stochastic Decomposition in Retrial Queueing Inventory System
Achyutha Krishnamoorthy,Dhanya Shajin +1 more
- pp 26
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The purpose of this paper is to obtain product form solution for retrial - queueing - inventory system and derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form.Abstract:
The purpose of this paper is to obtain product form solution for retrial - queueing - inventory system. We study an M/M/1 retrial queue with a storage system driven by an (s, S) policy. When server is idle, external arrivals enter directly to an orbit. Inventory replenishment lead time is exponentially distributed. The interval between two successive repeat attempts is exponentially distributed and only the customer at the head of the orbit is permitted to access the server. No customer is allowed to join the orbit when the storage system is empty and also when the serer is busy. We first derive the stationary joint distribution of the queue length and the on-hand inventory in explicit product form. Using the joint distribution, we investigate long-run performance measures and a cost function. The optimal pair (s, S) is numerically investigated.read more
Citations
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Journal ArticleDOI
On a queueing-inventory system with impatient customers, advanced reservation, cancellation, overbooking and common life time
TL;DR: In the particular case of Poisson process and exponentially distributed service time it is shown that the system admits asymptotic product form solution.
Journal ArticleDOI
On a queueing-inventory system with advanced reservation and cancellation for the next K time frames ahead: the case of overbooking
Dhanya Shajin,Achyutha Krishnamoorthy,Alexander N. Dudin,Alexander N. Dudin,V. C. Joshua,Varghese Jacob +5 more
TL;DR: The evolution of a system designed for reservation of some items in advance by customers arriving at random moments, including the special case of Poisson arrival, coupled with blocking of arrivals when all time frames are overbooked is shown to yield a product form solution.
Journal ArticleDOI
An M/M/1 Queueing-Inventory System with Working Vacations, Vacation Interruptions and Lost Sales
R. Manikandan,Sajeev S. Nair +1 more
TL;DR: With the system having infinite capacity, the stability condition for the system is obtained, followed by computation of the steady-state probability vector and discussion, and various performance measures are evaluated.
Journal ArticleDOI
Discrete Product Inventory Control System with Positive Service Time and Two Operation Modes
TL;DR: Analytical relations are established for the basic stationary performance characteristics of the Markov inventory control system and new orders are not admitted into the system, and the service process of the queued orders (if any) is stopped.
Journal ArticleDOI
A queuing-inventory model for manufacturing systems with fluid-type inventory
Jung Woo Baek,Yun Han Bae +1 more
TL;DR: In this paper , a make-to-order manufacturing system combined with a fluid-type inventory is considered, where customers arrive at the system to place an order for a customized product, thereby handling orders based on the first-come-first-served principle.
References
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Numerical investigation of a multiserver retrial model
Marcel F. Neuts,B. M. Rao +1 more
TL;DR: A simplifying approximation is made, based on understanding of the physical behavior of the system, which yields an infinitesimal generator with a modified matrix-geometric equilibrium probability vector that can be very efficiently computed even for high congestion levels.
Journal ArticleDOI
M/M/1 Queueing systems with inventory
TL;DR: In this paper, the stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales are derived.
Journal ArticleDOI
A survey on inventory models with positive service time
TL;DR: A detailed review of inventory models involving positive service time is given, including classical and retrial cases and directions for future work are indicated.